If $A$ is a skew-symmetric matrix of odd order, then $\det (A)$ is equal to:

Solution

1. For a skew-symmetric matrix, $A^T=-A$.
2. Taking the determinant of both sides, $\det (A^T)=\det (-A)$.
3. Since $A$ is of order $n$, $\det (-A)=(-1{)}^n\det (A)$.
4. Given $n$ is odd, $\det (A)=-\det (A)$.
5. This implies $2\det (A)=0$, so $\det (A)=0$. Hence the answer is (C).